Nevertheless, the sign of \(t\)  carries physical meaning independent of the choice of \(a \in \mathcal {J}(\mathcal {A})_\mathrm {sa}\) . To see this, we remark that inherent in Eq. (REF ) is the canonical identification between self-adjoint operators (observables) and generators of Jordan automorphisms (symmetry generators), \(a \mapsto \mathrm {ad}(ia)\)  for all \(a \in \mathcal {J}(\mathcal {A})_\mathrm {sa}\)  [1]}, [2]}, [3]}. Moreover, note that changing this identification to \(a \mapsto \mathrm {ad}(-ia)\)  results in a sign change for the parameter \(t\)  in Eq. (REF ), equivalently to a change in the commutator and thus to a change in the order of composition from \(\mathcal {A}\)  to \(\mathcal {A}^\mathrm {op}\)  in Eq. (REF ) (see also Lm. REF  below).
